Question

Right triangle has side lengths ,
, and . A second right
triangle, , has side lengths of 34, 30,
and 16. First, find the ratio of the side opposite
to the hypotenuse of triangle . Then,
use this ratio to identify the side length opposite
point on the second right triangle. (1 point)

Answers

GPT-4o mini
To solve this problem, we need to first identify the right triangles and their respective side lengths.

1. **Identify Triangle A**:
We need the specific side lengths of triangle A; however, they appear to be missing in your question. Usually, in a right triangle, we denote the sides as \( a \), \( b \) (the legs), and \( c \) (the hypotenuse). If you can provide the lengths, we can proceed.

2. **Identify Triangle B**:
Triangle B has side lengths of 34, 30, and 16. To find the hypotenuse, we can use the Pythagorean theorem:

\[
c^2 = a^2 + b^2
\]

Let's check that the hypotenuse is the longest side. We need to see if \( 34^2 = 30^2 + 16^2 \).

- \( 34^2 = 1156 \)
- \( 30^2 + 16^2 = 900 + 256 = 1156 \)

Since both sides are equal, 34 is indeed the hypotenuse of triangle B.

3. **Find the Ratio of Triangle A**:
Once you provide the lengths of the sides of Triangle A, we can calculate the ratio of the side opposite the hypotenuse. The ratio typically is expressed as:

\[
\text{Ratio} = \frac{\text{length of the opposite side}}{\text{length of the hypotenuse}}
\]

4. **Use This Ratio For Triangle B**:
The side opposite the hypotenuse in Triangle B is the longest side, which is 34.

After you provide the side lengths for Triangle A, I can help calculate the exact ratio for Triangle A and apply that to Triangle B.

Please provide the missing side lengths for triangle A so that we can complete the problem!